Spectra of random contractions and scattering theory for discrete-time systems

Random contractions (subunitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex eigenvalues of generic N × N random matrices  of such a type, corresponding to systems with broken time reversal invariance. Deviations from unitarity are characterized by rank M≤N and a set of eigenvalues 0<T _i≤1, i=1,..., M of the matrix $\hat T = \hat 1 - \hat A^\dag \hat A$ . We solve the problem completely by deriving the joint probability density of N complex eigenvalues and calculating all n-point correlation functions. In the limit N?M, n, the correlation functions acquire the universal form found earlier for weakly non-Hermitian random matrices.     

Sizing up the competition: quantifying the influence of the mental lexicon on auditory and visual spoken word recognition

Much research has explored how spoken word recognition is influenced by the architecture and dynamics of the mental lexicon (e.g., Luce and Pisoni, 1998; McClelland and Elman, 1986). A more recent question is whether the processes underlying word recognition are unique to the auditory domain, or whether visually perceived (lipread) speech may also be sensitive to the structure of the mental lexicon (Auer, 2002; Mattys, Bernstein, and Auer, 2002). The current research was designed to test the hypothesis that both aurally and visually perceived spoken words are isolated in the mental lexicon as a function of their modality-specific perceptual similarity to other words. Lexical competition (the extent to which perceptually similar words influence recognition of a stimulus word) was quantified using metrics that are well-established in the literature, as well as a statistical method for calculating perceptual confusability based on the phi-square statistic. Both auditory and visual spoken word recognition were influenced by modality-specific lexical competition as well as stimulus word frequency. These findings extend the scope of activation-competition models of spoken word recognition and reinforce the hypothesis (Auer, 2002; Mattys et al., 2002) that perceptual and cognitive properties underlying spoken word recognition are not specific to the auditory domain. In addition, the results support the use of the phi-square statistic as a better predictor of lexical competition than metrics currently used in models of spoken word recognition.     

Exterior powers of the reflection representation in Springer theory

Let H^*( B_e ) {H^*}\left( {{\mathcal{B}_e}} \right) be the total Springer representation of W for the nilpotent element e in a simple Lie algebra \mathfrakg \mathfrak{g} . Let Λ ⁱ V denote the ith exterior power of the reflection representation V of W. The focus of this paper is on the algebra of W-invariants in

Universal statistics of the local Green’s function in wave chaotic systems with absorption

We establish a general relation between the statistics of the local Green’s function for systems with chaotic wave scattering and uniform energy loss (absorption) and the two-point correlator of its resolvents for the same system without absorption. Within the random matrix approach, this kind of a fluctuation dissipation relation allows us to derive the explicit analytic expression for the joint distribution function of the real and imaginary part of the local Green’s function for all symmetry classes as well as at an arbitrary degree of time-reversal symmetry breaking in the system. The outstanding problem of orthogonal symmetry is further reduced to simple quadratures. The results can be applied, in particular, to the experimentally accessible impedance and reflection in a microwave cavity attached to a single-mode antenna.     

Theory of an induced-moment spin glass

We review the derivation of generalised TAP equations for general quantum spin systems and apply the theory to a simple induced-moment spin glass model. We consider two-level systems with a singlet ground state and a triplet excited state, which interact via long range random exchange couplings. For not too large energy splitting the spin glass state can be stabilised.     

Thermodynamics of the lanthanide halides I. Heat capacities and Schottky anomalies of LaCl3, PrCl3, and NdCl3 from 5 to 350 K

The heat capacities of LaCl₃, PrCl₃, and NdCl₃ have been measured from 5 to 350 K by adiabatic calorimetry. No co-operative thermal anomalies were seen in the temperature range investigated but substantial magnetic heat-capacity contributions of the non-cooperative (Schottky) type were found. Subtraction of the heat capacity of the diamagnetic and isostructural LaCl₃ from those of the paramagnetic members yields experimental Schottky heat-capacity contributions which are compared with heat capacities derived from spectroscopically determined energy levels. Small discrepancies between the calculated and experimental contributions are probably due to differences in lattice heat capacities between LaCl₃ and the others. The values of {(S^o(298.15 K) ? S^o(0)}/cal_th K^?1 mol^?1 are for LaCl₃ and NdCl₃, 32.88 and 36.67. Due to the possibility of a low-temperature phase transition, the entropy of PrCl₃ covers only the experimental range of this research and that of Colwell, Mangum, and Utton. {S^o(298.15 K) ? S^o(0.294 K)} for PrCl₃ is 36.64 cal_th K^?1 mol^?1.     

Experimental investigation into the convective heat transfer and system-level effects of Al2O3-propanol nanofluid

It has been speculated that the application of nanofluids in real systems could lead to smaller, more compact heat exchangers and reductions in material cost. However, few studies have been conducted which have carefully measured the thermo-physical properties and thermal performance of these fluids as well as examine the system-level effects of using these fluids in traditional cooling systems. In this study, dilute suspensions of 10 nm aluminum oxide nanoparticles in propanol (0.5, 1, and 3 wt%) were investigated. Changes in density, specific heat, and thermal conductivity with particle concentration were measured and found to be linear, whereas changes in viscosity were nonlinear and increased sharply with particle loading. Nanofluid heat transfer performance data were generally commensurate with that measured for the baseline. For the 1 wt% concentration, a small but significant enhancement in the heat transfer coefficient was recorded for 1800 < Re < 2800, which is attributed to an earlier transition to turbulent flow. In the case of high particle loading (i.e. 3 wt%), the thermal performance was observed to deteriorate with respect to the baseline case. Discoloration of the fluid was also observed after being cycled at high flow rates and increased temperature.     

Stimulus variability and the phonetic relevance hypothesis: effects of variability in speaking style, fundamental frequency, and speaking rate on spoken word identification

Three experiments were conducted to examine the effects of trial-to-trial variations in speaking style, fundamental frequency, and speaking rate on identification of spoken words. In addition, the experiments investigated whether any effects of stimulus variability would be modulated by phonetic confusability (i.e., lexical difficulty). In Experiment 1, trial-to-trial variations in speaking style reduced the overall identification performance compared with conditions containing no speaking-style variability. In addition, the effects of variability were greater for phonetically confusable words than for phonetically distinct words. In Experiment 2, variations in fundamental frequency were found to have no significant effects on spoken word identification and did not interact with lexical difficulty. In Experiment 3, two different methods for varying speaking rate were found to have equivalent negative effects on spoken word recognition and similar interactions with lexical difficulty. Overall, the findings are consistent with a phonetic-relevance hypothesis, in which accommodating sources of acoustic-phonetic variability that affect phonetically relevant properties of speech signals can impair spoken word identification. In contrast, variability in parameters of the speech signal that do not affect phonetically relevant properties are not expected to affect overall identification performance. Implications of these findings for the nature and development of lexical representations are discussed.     

Wetting phenomena on micro-grooved aluminum surfaces and modeling of the critical droplet size

The behavior of water droplets on aluminum surfaces with parallel grooves tens of microns in width and depth is considered, and a mechanistic model is developed for predicting the critical droplet size-droplets at incipient sliding due to gravity. The critical droplet size is nearly 50% smaller on micro-grooved surfaces than on the same surface without micro-grooves. The application of existing models fails to predict this behavior, and a new model based on empiricism is developed. The new model provides reasonable predictions of the critical droplet size for a given inclination angle, advancing contact angle, and maximum contact angle. When the grooves are aligned parallel to gravity, the maximum apparent contact angle does not occur at the advancing front but rather along the side of the droplet because of contact-line pinning. Droplets on these surfaces are elongated and possess a parallel-sided base contour shape. Novel data are provided for droplets in a Wenzel state, a Cassie-Baxter state, and combined state on micro-grooved surfaces, and the ability of the empirical model to handle these variations is explored. These findings may be important to a broad range of engineering applications.     

Magnetic properties of (Co Pd ) superstructures on Pd(100) and Pd(111)

The magnetic properties of (Co_nPd_m)_r superstructures on Pd(100) and Pd(111) are evaluated using the fully-relativistic spin-polarized screened Korringa-Kohn-Rostoker method. It is found that only in the case of a Pd(111) substrate such superstructures exhibit perpendicular magnetism, while on a Pd(100) substrate the magnetization is oriented in-plane. Also investigated is the effect of interdiffusion in repeated superstructures. By using the inhomogeneous coherent potential approximation (CPA) for layered systems the effect of ordering into (repeated) superstructures can be described in an ab-initio-like manner. It is found that already small amounts of interdiffusion can be decisive for the actual value of the magnetic anisotropy energy. Received 3 November 1999 and Received in final form 18 January 2000